Post on 20-Jul-2020
1
Multipoles and Coherent Gluon RadiationPlenary session
Lanny Ray, Univ. of Texas at Austin
STAR Collaboration Meeting LBNL 10/17/2013
Higher-order harmonics ?
BFKL Pomeron diagrams and v2
On to the LHC
Summary and Conclusions
2
Event 1
Event 2
ρsibling(p1,p2)
ρreference(p1,p2)
Correlation measure
:where
"" Gaussian) 2D side Same(
)2cos(2)cos(
, 1),(
),(
2
0
Model Fitting
n
QD
mix
sibch
ref
v
AAA
dd
dN
Fill 2D histograms
(1-2,1-2), (pt1,pt2)
Number of correlated pairs
per final-state particle
21
21
2
22
vd
dNA ch
Q
Relation between the
quadrupole amplitude and v2
3
What about higher harmonics, vn?Example: 200 GeV Au+Au 5-9%
No additional
model elements
required
Introduce a sextupole 2AScos(3); maintain away-side fit:
QD SQD QDSQD
net
sextupole
contribution
Same-side 2D peak = 1D ridge + reduced 2D Gaussian = Non-Gaussian 2D peak
Issue is description of the same-side peak. (LR, Prindle, Trainor, arXiv:1308.4367)
4
Non-Gaussian models of same-side 2D peak200 GeV Au+Au 28-38%
scale
x16
sextupole SS 1DG ridge NG exponents
polynomial poly+NG quartic
4
2
4
2
2D
2
4
4
2
2
2D
22
2D
2/
SSG
2
1exp
:Quartic
2
1exp1
:exponent NG or without with polynomial
2
1exp
:exponentsGaussian -Non
:ridgeGaussian 1D Side-Same22
A
A
A
eAevenk
k s
modelpeak 2D SS
Gaussian-Non
modelfit
Standard
scale
x16
Non-Gaussian models
Slight leptokurtic shape at 2-3 significance.
(LR, Prindle, Trainor, arXiv:1308.4367, accepted Phys. Rev. C)
5
Sextupole (v3) – one example of a NG peak
Reduction in
c2/DoF using
sextupole
The net effect of the sextupole (v3) is to allow a
small non-Gaussian shape for the same-side 2D
peak. It is not unique in that regard; other NG
models work as well or better. The only issue
here is the small NG shape of the SS 2D peak.
absolute c2/DoF
and using the
other NG models
(LR, Prindle, Trainor, arXiv:1308.4367, accepted Phys. Rev. C)
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ATLAS Pb+Pb 2.76 TeV 0 – 1%, pt = 2 – 3 GeV/c; (ATLAS, PRC 86, 014907 (2012))
These data do not require a sextupole! v3>0 fits can be forced but give poor c2.
Std. Fits with NG exponents, AQ < 0
ASG<0, no quad AQ ,AS<0 ASG, AS<0
Data Fit
(LR, Prindle, Trainor, arXiv:1308.4367, accepted Phys. Rev. C)
7
BFKL Pomerons - gluon interference
E. Levin and A. H. Rezaeian, Phys. Rev. D 84, 034031 (2011)
Two-BFKL Pomeron
Exchange with two-gluon
emission & interference
N
N
Multiple gluon emission from 2 or more
Pomerons interfere producing azimuth
anisotropy wrt momentum transfer
Resulting correlation:
Random emission results in uniform
dependence.
This mechanism was proposed to explain the
same-side ridge. However, it is a pQCD
prediction for a quadrupole correlation, or v2.
TQ
)2cos(
(Balitsky, Fadin, Kuraev, Lipatov)
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BFKL Pomerons & color-dipoles
Color Dipole Model: Kopeliovich et al.
Phys. Rev D78, 114009 (2008).
BFKL-saturation (glasma) model:
Dusling and Venugopalan,
arXiv:1210.3890
back-to-back
di-gluons
Quadrupole (v2)
(from Raju)
2v
9
May 2013 – http://indico.cern.ch/conferenceDisplay.py?confId=223909
MIT p+Pb Workshop – in honor of Wit Busza
Many, very interesting talks:
Miklos Gyulassy – “The Revenge of Wit : Will the Biblical Pillars
of AA 2003 be left Standing after the pA of 2013?”
10
11
12
13
14
15
But these questions have already been raised.
ST
Angular correlations –
jets, dijets (away-side)
not dissipated
Glauber superposition of
minijets (transparency);
large quadrupole (v2)
Constituent v2 – transverse rapidity
boost, non-hydro (Romatschke)
Quadrupole log(s)Nbin
scaling – initial-state only;
final-state effects ?
gluon-interference ?
All of this and much more
were known before p+Pb,
BES, LHC.
16
BFKL Pomeron Application to 200 GeV p+p(work in progress)
4
2
242
23,
2
2
3242t
tT
t
tT
tt
tqQp
t q
pQ
q
pQ
qp
qd
pdyd
dtTt
2cos12
14
22
t
Tt
q
Qp azimuthal
anisotropy
2
IPhN
Two-gluon density for
2-Pomeron exchange:
is the prob. for
two parton showers in a
N-N collision.
Construct correlations;
estimate momentum
integrals using the saturation
limit (QS):
15/
saturated-semi
~~ :saturation
for
llisionshowers/coPomeron No.
44 mQ
QqQ
Qp
n
T
StT
St
(Levin, Rezaeian PRD 84, 034031 (2011))
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Fit 200 GeV p+p frequency distribution
assuming 1, 2, … parton showers with
probabilities P1, P2, …
Mean Nch per parton shower equals the
minbias mean
Each shower produces a Poisson distribution.
P1 = 0.91, P2 = 0.09, P3 = P4 ~ 0
/5.2chN
Data (NBD)
1Pom
1Pom + hard
1&2Pom + hard (fit)
Poisson
P1 P2
BFKL Pomeron Application to 200 GeV p+pEstimate Pomeron probabilities:
ch
chh
chs
h
hsch
n
nn
nn
n
nnn
1
unit per 005.0 ,
hard soft ,
2(STAR, PRD 74,032006)
18
Prindle (STAR) ISMD-2013
STAR
Preliminary
Probability weighted
sum over 1 & 2
Pomeron diagrams;
pt-integral correlation;
Levin & Rezaeian QS2.
222222
84
42
4
4
2
4
42
22
1
21
2
ref
GeV 6.18.0,GeV 6.0 ,(GeV/c) 188.0 ,5.2/
sat-semi , 15/
saturated , /11
2cos22cos1
4
4
2|
mQpN
Qm
Q
Aq
QpPP
PN
Stch
S
S
T
QTtch
Quad
AQ = 0.0003 – 0.003; [semi-sat – saturated]
From D. Prindle (STAR) ISMD-2013 poster:
AQ = 0.002 for 200 GeV p-p NSD minbias; v2 = 0.072
Predicted Minimum-bias
quadrupole amplitude:
BFKL Pomeron Application to 200 GeV p+pEstimate p+p minbias quadrupole, v2:
2
22
vd
dNA ch
Q
19
Nch dependent quadrupole:
2cos15
1)(
2
pairs # total
pairs 2Pom correl. #
2
2
8
42
22
12
ref
ch
S
tchchch
ch
ch
n
Q
mpnnnP
n
n
QS2=0.6 GeV2
QS2=0.8 GeV2
Prindle (STAR) ISMD-2013
STAR
Preliminary
BFKL Pomeron Application to 200 GeV p-p
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Saturation limit
Semi-saturated, m2=1.6 GeV2
Semi-saturated, m2=0.8 GeV2
BFKL Pomeron Application to 200 GeV p-pNch dependent quadrupole:
Or, find QS for the three saturation assumptions in L & R:
Fit Data:
Solve for QS
2
000064.00007.0)(
s
chQ
s
ch nnA
n
n
Prindle (STAR) ISMD-2013
STAR
Preliminary
21
7 TeV p+p from CMS
CMS Collaboration,
JHEP 1009,091(2010).
TeV 7at 28at 008.0
:/ toconvertingafter obtain 034020] 84, D Rev. [Phys. Fits
1.0,110,
d
dNA ch
pNQ
ref
t
Quadrupole
22
Fit the CMS p+p NSD 7 TeV minbias
multiplicity frequency distribution data;
Mean nch/ = 6.0; assume ~ 0.02;
minbias average probabilities:
P1-4 = {0.67, 0.27, 0.06, 0.0}
P1
P2
P3
Data, || < 0.5
Fit with 1,2,3 P + nh
1, 1&2, 1,2&3 Pomerons,
no hard scattering
Pomeron Probabilities
BFKL Pomerons for 7 TeV p+p
Illustrative only!
Soft-hard decomposition
remains to do.
(CM
S,
JHE
P0
1,
07
9 (
20
11))
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BFKL Pomerons for 7 TeV p+p
222222
84
42
4
4
2
4
42
22
1
GeV 6.18.0,GeV 6.0 ,(GeV/c) 2.0 ,0.6/
sat-semi , 15/
saturated , /11
included showersPomeron 3 and 2 , 1
)1(2
mQpN
Qm
Q
qQpnnP
NA
Stch
S
S
T
Tt
n
nch
Q
Predicted range for AQ for 7 TeV p+p minbias: 0.006 to 0.05
Compared to 200 GeV minbias p+p: 0.0003 to 0.003
The increase is due to the larger pre-factor dNch/d, larger 2-Pomeron
probability, and the appearance of 3-Pomeron shower events.
Illustrative only!
Soft-hard decomposition
remains to do; as well as
QS estimates.
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5.02 TeV p+Pb at the LHC
ATLAS, PRL 110, 182302 (2013)
LHCat ]20,2[
.similar at (0.008) quadrupole
pp TeV 7 n thelarger tha4x -3
30 ,5 at 0.03-0.02 0,
:quadrupoleFit with
part
N
N
d
dNA
ch
chQ
Monotonic increase in same-side
-extension, ~ inc. quadrupole amplitude
In the BFKL-Pomeron model
typical high multiplicity p+Pb
collisions will have a couple of
multi-Pomeron events producing
quadrupoles.
Those quad. correlations add;
they do not cancel with random
orientation of each N-N scattering
plane: binN
QuadQuad NpAp )()(
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NN Superposition for 200 GeV p+Au
In Kopeliovich et al’s color dipole model v2 in p+A is computed from the singles anisotropy wrt
the p+A reaction plane. Random N-N orientation suppresses the net anisotropy and v2.
However, RP and EP are irrelevant for inclusive v2 measurements which equal the correlations
on relative azimuth.
In a Glauber superposition model quadrupoles
from N+N add linearly in p+A and A+A. Naively
we expect AQ(p+A) ~ AQ(NN,minbias) and
AQ(A+A) ~ (Nbin/Npart)AQ(NN,minbias).
p+Au Monte Carlo Glauber
Sample b, find Nbin
Sample p+p NBD and get nch(NN)
Use AQ(nch) to calculate (NN)
Sum to get (p+Au), Nch(p+Au)
and AQ(p+Au)
AQ(p+Au) increases with multiplicity
AQ,p+p(nch) ~ parabolic
~ linear
= constant
Predicted
Nch frequency
distribution
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6
10
20
NN Superposition for 200 GeV p+Au
The naïve expectation AQ(p+A) ~ AQ(NN,minbias) ~ 0.002 was not realized. Why?
To illustrate this I applied the MCG superposition model for larger numbers of N-N collisions.
Eventually, we recover the naïve expectation, however large quadrupoles persist at higher Nch.
The p+A quadrupole increases at
the upper end of the frequency
distribution because those events
are biased toward higher nch N+N
collisions, with larger AQ.
minbias),(NNAQ
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Summary & Conclusions
Higher-order harmonic (sextupole - v3) descriptions of 2D angular correlations are
actually describing small, non-Gaussian structure in the same-side 2D (minijet) peak.
The detailed structure of this peak is the real issue. Claims that these higher-order vn
have been “discovered” in the data are questionable.
Given the properties of angular correlations and the quadrupole in particular we may
ask if there is a pQCD explanation for v2.
The BFKL-Pomeron model of Levin and Rezaeian was applied to 200 GeV and 7 TeV
p+p frequency distributions and quadrupole correlations. Although there are large
uncertainties due to saturation scale estimates (QS), the quadrupole predictions are
consistent with recent data.
Further study and application of pQCD (BFKL Pomerons, color-dipole) to the
quadrupole correlations now observed in p+p, p+A and A+A at RHIC and LHC is
warranted.